Fiber-optic hydrophone is a key technology in underwater acoustic research and has significant advantages in practical application. It is widely used in AUV navigation and positioning, resource exploration, seawater warning and other scenarios. The optical fiber hydrophone transmits the sound signal into the light signal. The optical signal needs to be demodulated to extract the sound pressure signal when receiving the signal. Several common signal demodulation algorithms are summarized in this paper, including the PGC demodulation algorithm, 3×3 coupler demodulation algorithm and heterodyne demodulation algorithm. Then, the basic principles and improved technology of various demodulation algorithms are described with a summary and comparison of their advantages and disadvantages. Finally, the challenges that the demodulation technology of fiber optic hydrophone faces have been put forward.